FIG. 1 shows a principle of a structure for supporting a bobbin holder shaft in the prior art, in which reference numeral 1 designates a bobbin holder which is supported from a frame 5 via a bobbin holder shaft 2 and bearings 3 and 4. The bobbin holder 1 is mounted on the bobbin holder shaft 2 so as to be freely rotatable with said shaft 2 and has a known device (not shown) for holding the bobbin assembled therein, so that a yarn supplied while being traversed in the axial direction of the bobbin holder may be wound up on the bobbin to form a cheese-shaped wound yarn ball 6. In the case of the prior art winders, a supply speed of a yarn was of the order of 1500 - 2000 m/Min. at the fastest and an outer diameter of a bobbin was of the order of 150 - 200 mm, so that a rotational speed of a bobbin holder shaft could be of the order of 4000 rpm in use, and therefore, if a primary critical speed (i.e., lowest order resonant point) was preset at a value higher than 5000 rpm, then there remained no problem in practice. For that purpose it was only necessary to make a bobbin holder shaft thick and to make the bearing portion rigid for enhancing rigidity of the rotary shaft system including the bobbin holder. Recently, however, since a supply speed of a yarn of 3000 - 4000 m/Min., an outer diameter of a bobbin of 85 - 110 mm and a longer bobbin holder length have come to be required as an influence of innovation in technology, rationalization and campaign for enhancement of productivity, it has become very difficult to raise the primary critical speed of a bobbin holder shaft to keep it higher than the operating speed. In addition, the operating rotational speed now is as high as 10,000 - 15,000 rpm, so that it is impossible to preset a primary critical speed higher than the operating rotational speed as is the case of the prior art. In such cases, it has been considered effective to pliably support the bearings for the bobbin holder shaft to lower the primary critical speed of the bobbin holder shaft outside the range of and under the operating rotational speed region.
FIG. 2 shows the principle of a structure for pliably supporting bearings for a bobbin holder shaft as described above, in which reference numeral 7 designates a bobbin holder which is mounted on a bobbin holder shaft 8 so as to be freely rotatable with said bobbin holder shaft, which has a known device (not shown) for holding a bobbin assembled therein, and which is constructed so as to form a wound yarn ball 9 on the bobbin. The bobbin holder shaft 8 is supported by bearings 10 and 11, O-rings 13 and 14 made of rubber being pinched between the outer circumferences of said bearings 10 and 11 and a frame 12, and since the bobbin holder shaft 8 is supported elastically via the O-rings 13 and 14, the primary critical speed is lowered. However, in order to lower the primary critical speed under the operating rotational speed range according to this method, the elasticity of the O-rings 13 and 14 must be lowered to such degree that there may occur a practical problem. If this is practiced, because of the small elasticity of the O-rings, not only the bobbin holder 7 has its tip end cantilevered downwards by its own weight, but also the amount of downward drooping of the tip end will be increased gradually as the wound yarn ball 9 is formed, and thereby the shape and quality of the wound yarn ball 9 is adversely affected. Furthermore, because of the fact that the elasticity of the O-rings is extremely small, there is a disadvantage that the bobbin holder shaft will swing largely due to transient vibration generated upon passing through a lower order of critical speed, resulting in abnormal vibration exceeding the gap space c provided between the bearing 10 and the frame 12.
In addition, in the case of the transient vibration either upon passing through the lower order of critical speed or upon generation of a ribbon or a band on a wound yarn ball (See FIGS. 4 and 5), the self-damping effect of rubber caused by deformation of the O-ring is not sufficient as an attenuation effect that is effective for suppressing the amplitude of the transient vibration, so that it is impossible to maintain the shape and quality of the wound yarn ball good. Ribbons and bands are caused when the relation between a rotational speed A of the bobbin holder and a reciprocating frequency B of a traverse guide (not shown) satisfies A/B = N (where N is an integer). For instance, assuming that A = 500 rpm and B = 250 reciprocal cycles/Min., then we obtain A/B = 2, and for A = 2 rpm, B = 1 reciprocal cycle/Min is valid, which means that a yarn will trace the same route on a bobbin holder. A protrusion produced on a wound yarn ball from the above-mentioned reasons is called a ribbon 15. On the other hand, a band 16 is a protrusion generated in the neighborhood of A/B = N, where though a ribbon 15 is somewhat dispersed, the dispersion is not sufficient and a broad protrusion is produced.
FIG. 3 shows an equivalent vibration model for the apparatus shown in FIG. 2. In FIG. 3, k.sub.1, k.sub.2 and c, respectively, represent the elasticity and attenuation constant of the O-rings used at the bearing portions, w represents a weight of the bobbin holder, bobbin holder shaft and bearings, and W represents a weight of a wound yarn ball. Assuming now that a yarn is just before being wound on a bobbin, then W = 0 is valid, and the vibration model represents the state where a rod having a weight w is supported by two springs having elastic constants k.sub.1 and k.sub.2, respectively. The characteristic frequency at this moment of the vibration model has two values for lower order vibration modes where the rod is not bent, which correspond to a primary critical speed and a secondary critical speed, respectively, and therefore, it is only necessary to select the values of w, k.sub.1 and k.sub.2 so that said either critical speed falls outside of the operating rotational speed region of the winder. However, in the recent high speed type winders, the value of w is small because of the required specification and technical requirements, and so, unless the values of k.sub.1 and k.sub.2 are also reduced to a small value, the lower order of critical speed cannot be suppressed to a low value. Accordingly, even in case that only w exists, the springs are deformed and the rod not only sinks down but also tilts with its front end lowered, and further, as a yarn is successively wound and laminated and as a weight W is added, the tilting with the front end lowered becomes more remarkable, and the shape and quality of the wound yarn ball are also very adversely affected. In addition, in the case of the equivalent vibration model shown in FIG. 3, the damping effect is caused by the deformation of the O-rings and is thus small, and even if the primary and secondary critical speeds are preset outside of the operating rotational speed range so as not to generate resonance, attenuation of unstable vibration caused by transient vibration is weak, so that there are disadvantages such that deformation is given to a wound yarn ball, unbalanced excitation of vibration and displaced excitation of vibration are generated, and the quality of the yarn in the wound ball is deteriorated.